Medal and Fan! An inequality is shown below: -np-4

Question

Medal and Fan! An inequality is shown below: -np-4 < or equal to 2(c-3) Which of the following solves for n? A) n < or equal to - 2c-2 over p B) n < or equal to - 2c-10 over p C) n > or equal to - 2c-2 over p D) n > or equal to - 2c-10 over p

anonymous · Answer

@SolomonZelman

anonymous · Answer

I know its not C or D

misty1212 · Answer

$$-np-4 \leq 2(c-3)$$$$-np-4\leq 2c-6$$$$-np\leq 2c-2$$

anonymous · Answer

So we would than divide by p?

misty1212 · Answer

then divide by $-p$ but you cannot solve it because you do not know if $p$ is a positive or negative, but maybe it is supposed to be positive because it is called $p$

anonymous · Answer

So A :D

misty1212 · Answer

if p is positive then dividing by $-p$ means you have to change the inequality

misty1212 · Answer

$$n\geq \frac{2-2c}{p}$$

anonymous · Answer

Yes but in each of my choices there is a new negative sign that is before every single fraction :3

anonymous · Answer

So if we divided by -P it would still make the entire fraction negative correct :3

misty1212 · Answer

$$n\geq -\frac{2c-2}{p}$$

anonymous · Answer

Do we flip the sign each time?

anonymous · Answer

oh thats right when its a negative we do correct?

misty1212 · Answer

if you think $-p$ is negative then you flip the sign
your math teacher is not very smart though, because it could be that $-p$ is positive, like if $p=-2$ 
you cannot solve an inequality  with variable coefficients like that 
unless it says $p>0$ your math teacher should be ashamed of his learning